As disclosed in the co-pending patent application entitled: A Process for Non-Orthogonal NMR Imaging" filed: Aug. 27, 1985, Ser. No. 769,939, with Arthur Lim, Michael Buonocore, and Craig Barratt, as inventors, a technique of non-orthogonal NMR imaging is discussed. Because of non-idealities in the NMR system, such nonorthogonal imaging has been difficult to accomplish. The technique as described there involves forming by a digital method the various gradient waveforms and then by a digital to analog converter converting them to analog forms suitable for application to various gradient coils.
Such digital to analog conversion inherently involves a quantization error. In other words, the values of, for example, the phase encoding waveform amplitude must be rounded off to the nearest digital to analog converter (DAC) value. A common solution to this problem in the past, where merely orthogonal imaging was being accomplished, was to provide phase encoding steps of exact multiples of a DAC step size. This will not work in a non-orthogonal technique. However, even in a non-orthogonal technique, another solution is merely providing digital to analog converters with higher resolution; for example, 16 bit DACs versus 12 bit DACs. However, such converters must be high speed, glitch-free and have extremely good linearity; such converters are expensive. Thus, it is desired to be able to utilize a lower cost and lower resolution digital to analog converter and still minimize the effects of quantization errors.